In trucks having open box-type bodies, such as dump trucks for carrying particulate or discrete materials which can fall out of or be blown from the open body, truck covers are often employed to enclose the open body top to prevent such spillage and litter of the truck contents onto the highway and adjoining land. Government regulations often mandate the covering of open truck bodies for control of litter. Truck covers are generally known, as shown for example in U.S. Pat. Nos. 3,515,428, 3,549,197 and 3,549,199, in which a cover is retractably installed on a truck body and movable into open and closed positions. In the truck covers of the type shown in the above-noted patents, a cover sheet is rolled onto a shaft rotatable by a hand crank. The rearward edge of the cover is attached to a spring-loaded frame and upon unwinding of the shaft the frame draws the cover over the open truck top. The cover is composed of a canvas or other flexible sheet material and is supported only at the forward and rearward edges with the result that the cover can flap, especially in a strong wind, and can billow upward with the possibility of uncovering the truck top and permitting spillage of the truck contents.